An Alternative Way to Study 3-Way Data

An alternative way (AW) for the exploratory analysis of 3-way data is proposed. The approach is based on unfolding a three-way array, applying mode-dependent centering or scaling, and analysing the resulting structured two-way representations by principal component analysis. Rather than aiming at multilinear modelling or component resolution, AW is conceived as a variance-oriented exploratory strategy that provides complementary views of rows, columns and tubes using familiar PCA tools. The method generates six views that reflect different variance weightings and analytical perspectives, allowing interpretation to be guided by the experimental objective rather than by a single low-rank decomposition. The use of multiple views facilitates the identification of dominant patterns, the assessment of their stability across preprocessing perspectives, and the exploration of secondary effects associated with specific data modes. AW is illustrated using artificial and real three-way datasets, including chemically structured data. The results show that the relevance of each view depends on the scientific question under investigation; in particular, tubecentred views are especially informative when experimental conditions constitute the primary source of interest. Qualitative comparison with PARAFAC is used solely as an exploratory cross-reading of variance structures, highlighting conceptual correspondence in dominant patterns while acknowledging the different modelling assumptions underlying the two approaches. By combining conceptual simplicity, interpretability and flexibility, AW provides an accessible exploratory framework for three-way data analysis. It can be used as a complementary tool to guide interpretation and to support subsequent modelling choices in applied chemometrics and related fields.